The Hindu Mythology pays respects to Animals and treat them as a sacred Animals. many Hindu Gods like Hanuman , Nandi and Garud were Animals.
Lord Ganesha is blessed with a boon to be worshiped prior to all Gods by Lord Shiva . he is associated with two animals i.e the Elephant And Mouse.
ELEPHANT : Lord Ganesha has a face of elephant which also a Symbol of Big Brian , Lord Ganesha is the God of Wisdom.
Goddess Lakshmi , rides a white Elephant she is also worshiped as Gajja Lakshmi , Gajja is a sanskrit word for elephant.
Lord Indra the King of Devtaas (god) also ride an Elephant Airavat with three heads. Elephant is also a symbol of Samridhi . Elephants are worshiped in India ,and it is a very sacred Animal. Many temples in South India raise elephants as a property of their own , Some kings, Ministers and very rich people have a capability to donate Elephants in the temples.
Nandi : Nandi is an OX , Lord Shiva Rides Nandi. Nandi is booned by Shiva that who so ever recites a prayer in Nandi’s Ear it will surely reach Lord Shiva. Lord Shiva is Devo ke dev which means God of Gods. he is even called Mahadev , maha means the great and Dev means God.
Snake : Lord Shiva wear a Snake as a Garland around his Neck. Lord Vishnu sleeps on a SheshNaag. Krishna fought with Snake Kaliya ,who had 100 heads. when Krishna was born a snake Vasuki came to protect him from rain. Snake Vasuki also helped Matsay Avatar.
Mouse : mouse is called Mushak in Sanskrit. Lord Ganesha Rides on a Mouse. A story Related to Goddess Karni , an incarnation of Goddess Durga. Goddess Karni was born in Swaup village , she asked yama to restore life of son of a story teller , but yama was bund to his Dharma. Goddess Karni took a mid way between both the story tellers and Yama , she incarnated the dead son and all of the storytellers as a rat, under her protection. Her temple in Deshnog is filled with Rats and the Devotees offer them the food.
Monkey: Hindu God Hanuman is a monkey. Nal and Neel who built Raamsetu (Adam’s Bridge) were also monkey.
Mayur : Mayur is Sanskrit word for peacock . Lord Kartika, the second son of Goddess Parvati and Lord Shiva , rides a Peacock. Goddess Saraswati , the Goddess of Knowledge and wisdom, has a Garden full of Peacocks . Symbolically the feathers of Peacock is used for writing.
Garud : Lord VishnuRides on Garud. Garuda even helped Hanuman to protect the life of Sri Raam and Lakshman.
Krishna ride on Garuda to kill Narakasura. Lord Vishnu rides on Garuda to save the devotee Elephant Gajendra.